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Table 2 Formulas for the calculation of Hill diversity numbers

From: Knowledge, attitudes, and practices regarding vector-borne diseases in central Mexico

Index Formula Description
N0   Counts the total number of different opinions
Pi \( {P}_i=\frac{n_i}{N}\kern0.75em i=1,2,3\dots, C \) Where:
P = proportional abundance of the i-belief:
ni= frequency of the i-belief
N= total number of T beliefs
Pi is used to obtain diversity indices
Simpson’s diversity index (λ) \( \uplambda =\sum \limits_{i=1}^s{P}_i^2 \) Indicates the dominance of some ideas over others, this enabling the degree of agreement about a represented object in a community to be ascertained
Shannon-Weaver diversity index (H’) \( {H}^{\prime }=-\sum \limits_{i=1}^{S^{\ast }}\left({P}_{i\kern0.5em }\ln {P}_i\right) \) Where S is the known beliefs with proportions. Indicates the degree of complexity of the representation, wherein, as the number of opinions increases, the value of H’max tends to be higher
Hmax Hmax = ln N0 Maximum diversity of opinions
N1 \( \mathrm{N}1={e}^{H^{\prime }} \)
e = 2.71828
Indicates the number of abundant beliefs in the SR.
e is the base of natural logarithms and H’ is Shannon’s diversity index
N2 N2 = 1/λ Indicates the number of very abundant beliefs in the SR
Information index (I) I = Hmax − H Indicates the amount of information in the SR
Organization index (Q) \( Q=1-\left(\frac{H^{\prime }}{H_{\mathrm{max}}^{\prime }}\right) \) Indicates the degree to which the information is organized